About those militias

Jack Kelly argues that to succeed in Iraq we must take out Moqtada al-Sadr and his Mahdi army. Kelly notes that, following our failure to take Sadr out in 2004 (apparently on the theory that he wasn’t a major player), he has become “the most powerful figure in Iraq, eclipsing the more-or-less moderate Ayatollah Ali al-Sistani” and one with ties to Iran.
I agree that we made a major mistake by not finishing off Sadr in 2004. And it may be that we should correct that mistake, although the cost of doing so would be much greater now. But I wonder whether bringing down a given milita and/or its leader would make much difference at this point. My understanding is that the Shia militias exist mainly to inflict harm upon, and do battle with, the Sunnis. Given the “demand” for such units, it’s questionable whether we can cut off the supply.